There are two main approaches to obtaining “topological” cartesian-closed categories. Under one approach, one restricts to a full subcategory of topological spaces that happens to be cartesian closed… (More)

There are two main approaches to obtaining \topological" cartesian-closed categories. Under one approach, one restricts to a full subcategory of topological spaces that happens to be cartesian closed… (More)

We characterize the categories with finite limits whose exact completions are toposes. We review the examples in the literature and also find new examples and counterexamples.

We generalize Dress and Müller’s main result in [5]. We observe that their result can be seen as a characterization of free algebras for certain monad on the category of species. This perspective… (More)

Let M = (M,m,u) be a monad and let (MX,m) be the free M-algebra on the object X. Consider an M-algebra (A, a), a retraction r : (MX,m) → (A, a) and a section t : (A, a) → (MX,m) of r. The retract (A,… (More)

We give combinatorial proofs of the primary results developed by Stanley for deriving enumerative properties of differential posets. In order to do this we extend the theory of combinatorial… (More)

It is well known that for any monad, the associated Kleisli category is embedded in the category of Eilenberg-Moore algebras as the free ones. We discovered some interesting examples in which this… (More)

Motivated by an old construction due to J. Kalman that relates distributive lattices and centered Kleene algebras we define the functor K relating integral residuated lattices with 0 (IRL0) with… (More)

In analogy with the relation between closure operators in presheaf toposes and Grothendieck topologies, we identify the structure in a category with finite limits that corresponds to universal… (More)